China's reluctance to let markets play a freer hand in setting the value of the yuan, also called the renminbi, is a festering irritant that both the United States and China want to keep from getting out of hand.

China says it manages the yuan's exchange rate against a basket of currencies, but if there is a basket, the dollar is far and away the heaviest component. The history of China's managed float regime divides neatly into two parts: July 2005 to July 2008, when the yuan gradually rose 21 percent in a crawling peg to the dollar; and July 2008 to the present, when the yuan has been virtually repegged at about 6.83 to the dollar.

Since removing the yuan from a formal decade-old dollar peg in July 2005, Beijing has insisted that it is perfecting the exchange rate's formation mechanism, but the renewed rigidity over the past year has fueled growing anger abroad.

U.S. critics, especially business lobbying groups, complain that China has stopped the yuan from appreciating despite the Asian export giant's growing clout in the global economy.

China says that a stable exchange is an important help for its beleaguered exporters and that it also promotes stability in the global economy.

WHY DOES THE UNITED STATES OBJECT TO CHINA'S POLICY?

The Obama administration feels that Beijing's policy thwarts normal market adjustments that would push up the value of the currency of a rapidly ascending economy like China's, thereby making its products more expensive for foreigners.

As a result, China is amassing huge trade surpluses as well as swelling foreign exchange reserves as money pours in from sales of its products around the world.

IS THIS JUST AN ISSUE FOR AMERICA?

The International Monetary Fund has urged China to permit more exchange rate flexibility as an important part of efforts to rebalance global growth and as a way for Beijing to gain more autonomy in setting monetary policy.

European countries have also trekked to Beijing to urge it to let the yuan rise. Others that see their stores becoming outlets for Chinese-made goods have also cried foul.

They are running a great risk with this policy. It is a cause of some of the imbalances in the global economy. It is a contributing factor to some of the vulnerabilities that have existed and were realized, Bank of Canada Governor Mark Carney said recently.

WHAT WOULD HAPPEN IF CHINA LET ITS CURRENCY APPRECIATE?

Theoretically, the cost of Chinese-made products would rise for consumers around the world. If prices rise sufficiently, other countries' goods might be substituted for those China now makes. Some in the United States hope that domestic firms that now say they cannot compete might decide that they can boost their share of export markets, in turn cranking up production and hiring. If Chinese consumers were empowered with a stronger currency, they might become more aggressive importers, perhaps even swinging China's trade surplus to deficit.

In practice, though, the yuan's 21 percent rise from 2005-2008 barely registered on the price tags of Chinese goods abroad, as buyers -- often foreign firms like Wal-Mart -- demanded that costs be kept down and their suppliers were able to oblige, thanks in part to productivity gains.

Economists often describe China's trade surplus as structural, referring to the country's cheap capital and over-investment, which generate excess production that is cleared through exports. The implication is that deeper reforms to China's economy such as building up a social safety net, and not just yuan appreciation, are necessary to stimulate domestic demand and rein in its yawning trade surplus.

WOULD CHINA SERIOUSLY CONSIDER DUMPING ITS HOLDINGS OF U.S.

TREASURY SECURITIES?

China has amassed $2.27 trillion of foreign exchange reserves, the world's largest stockpile. The vast majority (analysts think about two-thirds) is invested in dollar-denominated assets. China is the single biggest holder of U.S. Treasuries, owning at least $776.4 billion of U.S. government debt at the end of June.

U.S. commentators fret that gives Beijing an effective tool to fend off U.S. demands for yuan reform by threatening to stop buying more debt and possibly selling what it holds. China has never actually uttered such threats, though it has for years said it is working to diversify its foreign currency holdings. Beijing, for its part, has expressed worries about Washington's massive and growing fiscal debt, as any resulting dollar weakness erodes the value of its American investments.

Apart from an extreme trade war scenario, it is unlikely that Beijing would ever dump its U.S. holdings as this would send shockwaves through the market and only serve to undercut the value of its remaining U.S. investments. Washington's ballooning deficit means that it needs investors to buy government debt more than ever, but, paradoxically, the scale of issuance means that China's share of new purchases has been getting smaller. As recovery from the financial crisis effectively forces the U.S. savings rate higher, domestic buyers have become the most important source of incremental demand for Treasuries, making the United States relatively less vulnerable to changes in foreign demand.

WHAT WOULD BE THE CONSEQUENCES OF A SELL-OFF OF U.S.

GOVERNMENT DEBT?

If the single largest buyer of U.S. government debt -- China -- sold it off or vowed to buy no more, the immediate impact would be downward pressure on the dollar. One of the United States' strongest claims for the dollar's status as a key reserve currency is that it runs the deepest, most liquid capital markets in the world, so if its top buyer dropped out, that claim would ring hollow and the dollar's status would be called into more serious question than it is already.

(Reporting by Glenn Somerville and Simon Rabinovitch, editing by Stacey Joyce)